Cambridge International AS and A Level Mathematics Pure Mathematics 1

Algebra

P^

1

EXAMPLE 1.10 Simplify

3

5

5

6

x^2

y

yz

× x.

SOLUTION

Since the two parts of the expression are multiplied, terms may be cancelled top

and bottom as in arithmetic. In this case 3, 5, x and y may all be cancelled.

Expression

EXAMPLE 1.11 Simplify

(– )

(– )

x

xx

1

41

3

.

SOLUTION

(x − 1) is a common factor of both top and bottom, so may be cancelled.

However, x is not a factor of the top (the numerator), so may not be cancelled.

Expression = (–x )

x

1

4

2

EXAMPLE 1.12 Simplify 3424 ()xx++^61.

SOLUTION

When the numerator (top) and/or the denominator (bottom) are not factorised,

first factorise them as much as possible. Then you can see whether there are any

common factors which can be cancelled.

Expression = 6434 ()()xx++^11

= 2

EXERCISE 1A 1 Simplify the following expressions by collecting like terms.

(i) 8 x + 3 x + 4 x − 6 x

(ii) 3 p + 3 + 5 p − 7 − 7 p − 9

(iii) 2 k + 3 m + 8 n − 3 k − 6 m − 5 n + 2 k − m + n

(iv) 2 a + 3 b − 4 c + 4 a − 5 b − 8 c − 6 a + 2 b + 12 c

(v) r − 2 s − t + 2 r − 5 t − 6 r − 7 t − s + 5 s − 2 t + 4 r

=×

=

3

5

5

6

2

2

2

x

y

yz

x

xz